Sets of singular restrictions of symplectic forms

Abstract

Let $\Omega$ be a non-singular syplectic form on some vector space $V$. Denote by $S_k^n(\Omega )$ the set of all $k$-dimensional planes $s$ in $V$ such that the restriction of $\Omega$ onto $s$ is singular. For the cases when $k=2,n-2$ a simple geometric characteristic of $S_k^n(\Omega )$ will be described.

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